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AnnZ [28]
3 years ago
13

A triangle was dilated by a scale factor of 6. If sin aº

Mathematics
1 answer:
Pavlova-9 [17]3 years ago
8 0

Answer:

24 units

Step-by-step explanation:

A triangle was dilated by a scale factor of 6. If sin a° = four fifths and segment DE measures 30 units, how long is segment EF?

triangle DEF in which angle F is a right angle, angle D measures a degrees, and angle E measures b degrees

15.5 units

24 units

30 units

37.5 units

From the description:

angle D measures a degrees

opposite to angle D is side EF

side DE (which measures 30 units) is the hypotenuse of the triangle.

We also know that

\sin (a) = \frac{4}{5}

\sin (a) = \frac{opposite}{hypotenuse}

From definition:

\sin (a) = \frac{opposite}{hypotenuse}

Replacing:

\frac{4}{5} =\frac{ EF}{DE} \\\\EF = \frac{4}{5} *DE\\\\EF = \frac{4}{5} *30 \\\\= 24 units

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